For the calculations presented in this paper, we assume \(\epsilon _{\uparrow } - E_{\rm {F}} = 3.0\)  eV, \(\epsilon _{\downarrow } - E_{\rm {F}} = 5.6\)  eV for the T ferromagnetic layer (free layer) with spin quantization axis along the \(\textbf {x}^{\prime }\)  direction and \(\epsilon _{\uparrow } - E_{\rm {F}} = 3.0 + \delta \)  eV, \(\epsilon _{\downarrow } - E_{\rm {F}} = 5.6 + \delta \)  eV for the B ferromagnetic layer (fixed layer) with spin quantization axis along the \(\textbf {x}\)  direction, where the Fermi level is fixed at \(E_{\rm {F}} = 0\)  eV and the parameter \(\delta \)  controls the asymmetry between the magnetic layers [1]}, [2]}, [3]}. Additionally, the tunnel barrier is assumed to be composed of \(N = 3\)  atomic planes with onsite energies \(\epsilon _{\uparrow } = \epsilon _{\downarrow } = 9.0\)  eV and the hopping parameters assume the values \(t_{\uparrow } = t_{\downarrow } = -1.0\)  eV. The particular choice of parameters provides a good estimate of the right order of magnitude of spin torques, exchange coupling and tunneling magnetoresistance (TMR) of Fe/MgO/Fe MTJs [4]}, [5]}, [6]}.
